CAS Exam MAS-I Fall 2018, Question 33
Study guide: Exam MAS-I
Two ordinary least squares models were built to predict expected annual losses on Homeowners policies. Information for the two models is provided below:
Model 1
| Parameter | \hat{\beta} |
p-value |
|---|---|---|
| Intercept | 212 | |
| Replacement Cost (000s) | 0.03 | < .001 |
| Roof Size | 0.15 | < .001 |
| Precipitation Index | 120 | 0.02 |
| Replacement Cost (000s) x Roof Size | 0.0010 | 0.05 |
Model 1 statistics: R^2 = 0.91, Adj R^2 = 0.87, MSE 31,765, AIC 25,031.
Model 2
| Parameter | \hat{\beta} |
p-value |
|---|---|---|
| Intercept | 315 | |
| Replacement Cost (000s) | 0.02 | < .001 |
| Roof Size | 0.17 | < .001 |
| Number of Bathrooms | 210 | 0.03 |
| Replacement Cost (000s) x Roof Size | 0.0015 | < .001 |
Model 2 statistics: R^2 = 0.94, Adj R^2 = 0.89, MSE 30,689, AIC 25,636.
| Cross Validation Set | Model 1 MSE | Model 2 MSE |
|---|---|---|
| 1 | 33,415 | 26,666 |
| 2 | 38,741 | 38,554 |
| 3 | 32,112 | 39,662 |
| 4 | 37,210 | 36,756 |
| 5 | 29,501 | 30,303 |
You use 5-fold cross validation to select superior of the two models.
Calculate the predicted expected annual loss for a homeowners policy with a 500,000 replacement cost, a 2,000 roof size, a 0.89 precipitation index and three bathrooms, using the selected model.
- A) Less than 1,000
- B) At least 1,000, but less than 1,500
- C) At least 1,500, but less than 2,000
- D) At least 2,000, but less than 2,500
- E) At least 2,500
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